Changing Hosting Company

I have a client who wants to change hosting.Right now he is using PLESK.
I will change DNS to point to my shared hosting (hostgator).

1-from where do i need to change DNS settings from within PLESK or domain registrar?
2-domain registrar and PLESK are two separate things (I know with CPANEL it is) the reason i ask is inside PLESK I see domain dns change settings,…
3-when i do domaintools i see Registrar:
Name: Tucows.com Co.
Number: 156

what this means?

thank you

Hi,
The DNS are changed to domain registrer, and can take up to 24 hours to propagate.

Thanks for your reply.

i will host a website right now they are on Plesk. Do i need to change dns inside plesk or inside domain registrar?

so plesk has nothing to do with it,i just need to change domain registrar to point to my hostgator cpanel correct?
what confused me when i logged in in plesk i saw dns settings i thought everything is there.
So plesk dns settings and domain registrar settings are 2 separate things.
domain registrar is the one we need to change to point a domain site to our new hosting?correct?

thanks

Basically, logg in on the web site where you registered that domain. In your account, find something about DNS settings to that domain and add the new dns, provided by hostgator.

Once you have purchased a hosting with another provider then just change the name server to new hosting company . This can be done from domain registrar end. And also you can contact your new hosting provider to transfer website content from old hosting provider to new one.